Art of equalizing stresses in structural elements



June 16, 1931. V 1,810,232

ART OF EQUALIZING STRESSES IN STRUCTURAL ELEMENTS Filed April 14, 1928 2 Sheets-Sheet l f CUMPRESS/VE 577955556 a, COMPRESJJl/E 157 PES$E5 flew-SHE Gav/7 541 v:

C fl/VPRESS/ v5 STRESsss Q/w-FP June 16-, 1931. VOGT 1,810,232

14, 1928 ZSheet Sh t 2 fir s fred/i/a Vqyt [7111622 for Patented June 16, 193i UNITED STATES P.

r orrica FREDRIK VOG-T, OF TRONDHJIEM, NORWAY, ASSIGNOR OF ONE-.EALF T E. C. LA' RUE AND B. F. JAKOBSEN, DE LOS ANGELES, CALIFORNIA, DOING BUSINESS AS LA R UE & JAKOIBSEN Application filed April 14,

This invention has to do with the art of structural elements or bodies such as are typically composed of concrete. The invention in its present practical applicationis aimed 'more particularly at such structures as concrete dams; but from a consideration of the general nature of the invention itwill be clearly understood that it is not limited in applicability to dams,but is-broadly applicable to various sorts of structures and elements which, under load, are subjected to stresses nonuniform across their cross sections; therefore it will be readily understood that the invention is not necessarily limited to elements or. structures composed of con crete or any similar substances. It is only because the invention has a major utility as applied to. concrete dams, and because its general principles, mode of operation and final results can perhaps be best explained and understood in connection with dam structures, that I choose to explain itspecifically as applied to concrete dams. Thus, using a concrete danias a basis of this description, I shall first briefly note the conditions obtaining in ordinary structures of that type andthen briefly explain how my invention is applied.

Take a typical dam structure of the arch or gravity type or of a combined arch and gravity type. It is to be noted that when the dam structure is completed and before it is subjected to water pressure on its up-stream face, the structureis subjected to substantially no stresses except gravitational stresses and those resulting from contraction of the concrete due tosetting and temperature changes. Initially in this discussion, such stresses, al.- though present, may be temporarily disregarded, although in thefinal-analysis they are taken into consideration in the determination of the effective counter pressures which are applied in my system. Let us -consider first the stresses produced in a concrete dam under water load. Takin for instance a dam of the combined archan gravity type, or a dam of any type for that matter, the water pressure exerted on the up-stream face tends to displace the center portions of the dam in to a down-stream direction. Presuming that ART OF EQUALIZIN' G STRESSES IN STRUCTURAL ELEMENTS 192s. Sbrial No. 269,930.

such a dam is rigidly supported at the side abutments, then viewing the dam as a beam or as an arch, such down-stream displacement tendencies set up considerable com ressive stress at or near the-center or orownao the upstream face, and a lesser compressivestress or even a tension, at or near the center or crown of the down stream face; But at or near the abutments the stresses set up are,relatively speaking, reversed; that is, relatively high compression is created near the abutments at the down stream face while a relatively low compression or even tension is created near the abutment at the'up-stream face. And at any vertical cross-section between the center,-or crown, and the abutment's, the'relation of stresses varies accordingly, there being a cross-section at some place between the center or crown and each abutment where stresses are substantially equalized over the whole crossssection.

Without the necessity of neering and technical details regarding the imposed stresses and their modes of calculation, the foregoing states in a general way the broad relation of stresses set up in any structural element such as a dam, when 'c'onsid ered as an arch or beam, Such considerations also apply broadly to the stresses set up in beams fixed at'the ends and subjected to any kind of load, as will be readily recognized. And from a consideration of that similarity between the action of a dam and the action of a beam or arch, it will be seen how my invention 1s generally applicable to various kinds of structural elements which carry posed loads, for the purpose of equalizgoing i t e s to the structure as a beam or arch, but also as forming, or being formed of, a cantilever or series of cantilevers resting upon the foundation. The cantilever action of the-dam, like .its beam'or arch action, Will of course tially vary. Furthermore the general rela- .a finished dam structure when tionship of stresses upon different dams will also va in accordance as to whether the dam is 0 substantially a pure arch type or of substantially a pure cantilever type, or of a mixed type. But'in any case and whatever the conditions may be, it is ssible and practicable, at least with sufliclent accuracy for all practical purposes, to ascertain beforehand what stresses will be developed within subjected to water load.

Generally speaking, the ascertained horizontal stresses are found to vary in different parts of a dam structure and are found to be non-uniform over all of the vertical crosssectional areasof the dam except perhaps on two cross-sections located between the center or crown and the abutments. Typ1- cally it is found' that at the crown crosssection there will be, as I have said before, a relatively high compressive stress at the up stream face and a relatively low compressive stress, or even a tensile stress, at the downstream face. And conversely, at an abutment section high compression is found at the down-stream face and low compression or tensile stress at the up-stream face. It is thus typical that the stresses at a crosssectional area are not uniform, that limited portions of the dam structure are subjected to much higher compremive stresses than are others, and that therefore the whole comressive force to which a dam is subjected 1s in effect carried disproportionately by a limited part of its structure.

It is a general object of this invention to provide a system stresses may be equalized or substantially so, thereby to increase the effectiveness and strength ofa given structure and thus either to increase its factor of safety under a given load or to enable the structure to be out down in dimensions to support a given load with the same factor of safety as before, with obvious economic advantage. accomplishes this purpose by a system which I may term a system 'of multiple pressure grouting. And, as applied particularlyio concrete dams, the invention has a further object and corresponding accomplishment in that it avoids the necessity of allowing a completely formed dam structure to stand whereby such compressive.

The invention over a long period of time, as required at present, before it can be grouted.

In the construction of concrete dams as practiced at the present time the concrete is poured and formed usually in sections, the sections being separated from each other by joints in vertical cross-sectional planes. After formation is completed the concrete structure must then be allowed to set and cure for a considerable period of time, sometimes as long as two or more years, before the concrete has sufliciently contracted and the joints opened up. Then the joints are grouted under no pressure except that due to the weight of the grouting material. Such a dam, however, is subjected to all of the differential stresses which I have before described. Usually and generally, grouting of such a dam is not attempted until sufficient contraction has taken place to open up the joints widely enough so that grout can flowed into them. Even if the joints had been initially left wide enough open that grouting could be performed immediately after the dam had been cast, and even if grouting were performed at pressures high enough initially to displace the dam in a direction up stream by the same amount that it will subsequently be displaced down stream by the water load-even then when the dam is placed under water load the various crosssectional areas will be subjected to differential stresses and the dam will therefore not I carry the load which it is capable of carrying under my system.

- Under my system of operation the routi is applied to the joints under di erentiifi pressures at different parts of each cross sectional area, such differential pressures being calculated to offset the differentials due to the final application of water pressure on the upstream ace, variations of tem erature, time effect and shrinkage arising fi'om setting. The resultin variable stresses in each cross-section being own, the grouting is applied at each such section inaccordance with those ascertained variable stresses; the result bein that when the water load is finally applie the stresses throughout the dam structure are substantially uniform. And this provision for control of grouting pressures leads to the result that in my s stem I can grout a dam immediately after 1t is formed and without waiting for the final contraction of the concrete either for grouting or for putting the dam into use.

- In making a practical application of m system, I not only provide for ap lying di.

vide for applying differential pressuresat vertically spaced points in any cross section, or joint; thus to provide for the application of the pressures not only to suit the difference in stresses between. horizontally spaced Figurel is a diagrammatic plan on which typical stress diagrams are shown.

Fig. 2 is adiagrammatic elevation showing contraction joints; 7

Fig. 3 is a diagrammatic vertical cross section indicating a typical sub-division of the joint spaces for thepurposes of my system.

Figs. 4, 5 and'6 are horizontal cross sections showing 'difierent' typical forms of joints that may be used.

Fig. 7 is a vertical cross section across a joint s owing a typical form of joint.

Figs? 8; 9 and v10 are stress diagrams illustrating certain points made in the specification. Y

Merely for the purpose of explanation, I am assuming a dam of the kind shown in the I drawings, and assuming that the dam structure is divided into several sections (typically these sections can be from to 50 feet long), the sections meeting at the vertical contraction joints generally indicated by the letter J, in Figure 2, and shown in typical detail in Figures i to 7, The several vertical joints J become, in my system, the cross sectional areas on which pressures are applied; and for the purpose of applying differential pressures to different points in each cross sectional area the joints are divided by suitable stops, a general and typical location of which are indicated in diagram in Figure 3, where the water stops are shown in dotted lines and generally designated by the letters S for the vertical stops and S1 for the horizontal stops.

By the horizontal. stops the dam may be regarded as being divided into several horizontally extending zones between the horizontally extending stops; or ear-h vertical contraction joint may be re arded as being divided not only laterally ly the vertical stops S, but also vertically by the horizontal stops S1. Thus in the diagram of Figure 2 the dotted lines S1 represent possible planes 7 of location of the horizontal stops in such relative positions as shown in Figure 8.

In order efiectivelyto apply my system, and to be able to apply it without waiting for contraction of the concrete, the joints J are constructed in some manner such as to make thenr comparatively open either over substantially the whole of their areas or at least parts of their areas. Thus, as shown in Figure 4, the vertical joints may be constructed so as to leave an open grouting space oversubstantially their entire areas, the grouting spaces being stepped and divided by'the vertical stopsS so that there is then provided in efi'ect a series of separated groutingspaces G,-to which differential and individual, pressures may be independently applied. On the other hand, as shown inFigures 5 and 6, the open grouting spaces G may be made to extend only over art of the joint area, the

other parts of the oint area being in close contact. The number of separate grouting spaces thus provided may, of course, be as many or as few as is necessary or desirable. Likewise these individual grouting spaces may be subdivided vertically into as many separate spaces as may be desired or necessary under any circumstances. Such vertical subdivisions are indicated in Figs. 2 and 3, in which figures horizontal water stops S'l stop 0d and divide the several individual grouting spaces G from each other.

The manner in which these grouting spaces are formed, the type and structure of forms used, and other details need not here be explained as the method of construction or formation will be readily understood by those skilled in the art. It, is only necessary here to observe that the physical construction of the dam may be carried on in any of the usual manners and that the ressure application to the lower parts of t e dam need not be postponed until the upper parts are finished. The vertical subdivision of the grouting spaces enables the grouting to be carried on step by step as the dam is built, if so desired. And such step by step grouting may in many cases be desirable because thereby the lower completed parts of the dam are placed under their permanent stresses before the weight of the super-im pansion of the. concrete due to the addedvertical weight pressures.

However, for purposes of explanation I shall consider that'the dam is finished before the grouting is performed. Immediately the dam is finished, it may be grouted without any delay and the grouting is then carried on under such differential pressures applied to the several separate grouting spaces, as to accomplish the purposes desired in the manner which I have before set forth. Prior to or coterminously with the grouting operations the several individual joints orgrouting spaces may be subjected to water pressure; and such use of water pressure preliminary .to the grouting operations is ordinarily highly desirable, because water pressures similar to the final grouting pressures may be first applied to all of the grouting spaces and thus to all of the joints, or to those spaces and joints near the particular sections to which the grouting is being applied at'a given time, putting the whole structure, or a considerable part of it, under the various applied stresses which are desired, and holding the structure as a whole plied to typical cross sections.

under those stresses while the individual joint spaces are grouted. That procedure not only has the advantage that the structure is not merely subjected locally to the applied pressures, but also has the advantage that preliminary water pressures may be used for some time before the actual grouting takes place, the water helping to cool the concrete to take away the heat of setting, and acting to keep the dam under the applied pressures during its setting operations.

Furthermore, this preliminary use of water has the advantageous result of maintaining the space-defining walls well moisten'ed, so the grouting may be subsequently applied with greater facility and effective-' ness as will be readily understood. As a still further feature, though this is not essential to the carrying out of the system, I may provide means for circulating water through the open joints before the grouting operation (whether or not the application of differential water pressure is utilized) to hasten the cooling of the concrete, thereby rendering it, at the time of subsequent grouting, nearer its ultimate condition, to obvious advantage. For cooling by water circulation, it is of course immaterial whether the joints be subdivided into several separated spaces.

Such applied water pressures may be applied to the individual grouting spaces in the same manner as the grouting is subsequently done; and both pressure applications may be effected through the means of any suitable individual connections with the several independent spaces. For instance in Figures 3, 4 and 5 I have shown individualpipes P L which lead to theseveral separated spaces, preferably near their tops.

Preferably I provide valved drain or circulation pipes T leading from the several separated spaces near their bottoms. With the drain pipes open, Water may be circulated through, the spaces, to the end set forth above; and then after closing the drain pipes, the differential water pressure may be applied. When the grouting is to be applied the outlets are, of course, first opened to drain the water, and subsequently closed so the differential grouting pressure may be set up.

I have indicated heretofore how the grouting pressures are calculated and applied in such manner as to offset the difierent stress pressures which are developed by the water load and shrinkage and so as to equalize such pressures as far as may be practicable, over the cross sectional area. I have indicated that the variations in such pressures will be different in different structures. But for purposes of typical explanation I have shown in Figure 1 typical stress diagrams ap- These stress diagrams will need no detailed explanation in view of what Ivhave said. The typical stress diagram at the crown or cenwere introduced to the joint J over its entire face, the uniform applied grouting pressure being indicated at U in the diagram. It is seen that the final pressures at the joint are still non-uniform, and to the same extent as they were initially. In Fig. 10, the pressure existing before my system of grouting is applied is shown by R and R The different grouting pressures applied to sections G, G and G are shown by U U and U, respectively. In this diagram it is assumed that the grouting pressure U applied over the individual area G1 is small or relatively small, so that the final pressures over that area remain substantially the same as they were in the diagram of Figure 8. To the area G2, Fig. 10, uniform pressure, represented by U2, is applied and to the area G3 a higher uniform grouting pressure, represented by U3, is applied. The result then becomes, as represented in Figure 10 that the final pressures over the whole joint area are much more nearly uniform than is possible under the systems represented in Figures 8 and 9.

One structural feature to which I wish to call further attention is shown in Figures 5, 6 and 7. As shown in Figure 4, the-joint J may be opened substantially over its entire area or face, and subdivided by suitable water stops. However, if as shown in Fi ures 5, 6 and 7, the joints are partly open and partly closed, limited bearing faces are provided as indicated at F, which makes provision for suflicient compressive strength at the joints so that even the full water pressure, if desired, may be applied to the dam before the pressure grouting is applied or completed.

Of course, in no case, in my system is precise uniformity obtained because it is not practical to subdivide the joints into an infinite number of separate areas; but in practice it is sufficient to subdivide the joints into a few separate areas. In fact, in many instances, it may be suflicient to provide, in a i) givenjoint, only one open joint area for the entire face of a joint, or only one open joint area so placed in the joint face, that pressure grouting will obtain the beneficial results which have 'hereinbefore been described. Although it is preferable to divide each joint face into a number of separate open grouting spaces for application of selected pressures, certain beneficial results, due in general to simple pressure grouting, may be had in my system even though only a single open joint space is used in all joints. The important feature of my invention in this regard lies in its structural provision of a definitely open grouting space to which pressure grouting may be applied fully and completely and under full pressure over the whole or substantially the whole face of the joint and without waiting for the concrete to contract. g any case, and whether or not each joint is bdivided into several separate spaces, the final resultant pressures will vary somewhat over each separate and individual area; but the total pressures on each individual area (assuming for the moment that all of the separated areas are individually of the same size) will be substantially equal. And fur thermore it is to be noted that the variation in pressure within each area is not so marked as the diagram of Fi ure 10 would seen to indicate. The final e ective pressure line is in practice not a sharp angular line such as shown here, but in practice is more like the dotted line shown at V3, especially at a short distance from the joint.

Just as proper individual pressures may be applied to the several laterally separated areas, also proper individual pressures may be applied to the several vertically separated areas; so that in the final gr'outed structure the stresses and pressures are not only made substantially uniform as regards horizontal distributions, but also made consistent as regards vertical distributions as far as that is wished. No further detailed explanation is thought to be necessary, as the manner in which such uniform or graduated or consistent distribution, both horizontally and vertically, will now be well understood by those skilled in the art.

In some dams a division of the joints for the purpose of grouting with difierent press lres is only necessary for a few of the joints,

say one at the crown and one at eachabutment, or even only for one at the crown; while the other joints may be grouted in advance without pressure or only with a slight pressure. For other dams a pressure grouting in a greater number of joints may be necessary to obtain good results, that depending mainl on the shape of the dam site and the size 0 the dam and other factors, and must be decided for each individual case.

Furthermore, and although I have spoken of the pressure grouting primarily as a means of substantially equalizing or rendering substantially uniform, the stresses throughout such structures, itwill be now readily understood that the system is not at all limited to what may be strictly termed equaliza-' tion of pressures; but that it is the general object and its final function is, more broadly speaking, to modify pressures in such structures so as to make the final stresses smaller nee less than they otherwise would be and more uniformly consistent with the theoretical stresses which should be borne by difi'erent parts of the structure in order to bring the structure as awhole to or near its highest point of efliciency. For instance, in the case of straight or slightly curved dams, the beam or arch eflect in the dam, considered asa beam or arch between the two abutments, can be less for a uniform than for a non-uniform (unequal) distribution of the horizontal stresses. At the same time: the beam or arch effect obtained by grouting of the joints without pressure for such dams is usually rather unimportant, so that the strength of the material is not utilized by the horizontal stresses, while on the other hand the cantilevers have to take almost all the load. To reduce the load taken by the cantilevers for such dams and at the same time to utilize the strength of the material as regards horizontal stresses, a pressure grouting in some divisions of the joints can be applied in such a way that the non-uniform distribution of the horizontal stresses due to water pressure is exaggerated up to what is found to be a suitable limit for the stresses inv the material used in the dam. In other words, the secondary arch in such a dam may be considered in applying the grouting pressures. Whether modification of the stresses in the arch, or groutingof the kind here described, ought to be used, depends in any case upon the curvature of the damin question and must be decided for each individual case. Consideration of all the foregoing will now ake it clear that using the words equalize nd equalization it must thus be understood that I do not mean that all stresses (either as regards vertical or horizontal distribution) are made to be equal, in the sense of being the same; but that I mean equalization in the sense of equitable distribution having regard for the stresses and pressures to be carried, and that, in general, I reduce the otherwise maximum stresses and/or increase the. otherwise minimum stresses, to the final effect that the load carrying capacity of a given structure is enhanced.

I regard my invention as fundamental and broad, both as a system of procedure and as a system of construction. The following claims, therefore, deal with the invention, both as regards method of procedure and as regards structure.

I claim:

1. Themethod of equalizing stresses in a load carrying structure which is subjected to a non-uniform distribution of stresses over a sectional area, that includes forming over such cross-sectional area a joint opening having sub-divisional enclosed pressure receiving spaces, and applying and holding diflerent pressures respectively and separately on the several pressure receiving spaces, the pressures bein such that the stresses to which that portion of the structure is subjected will be substantially uniformly distributed across the face of the 6 cross-sectional joint area.

2. The method of equalizing stresses in a .load carrying structure which is subjected to a non-uniform distribution of stresses over a sectional area, that includes forming over such cross-sectional area joint openings having sub-divisional enclosed pressure receiving s aces, applying grouting material under di erent pressures respectively and separatel to the several pressure receiving spaces, t e differential grouting pressures being such that the stresses to which that portion of the structure is subjected w ll be substantially uniformly. distributed across the face of the cross sectional joint area, and maintaining the grouting under said pressures in said spaces until it sets.

3. The method of building a concrete dam or the like, that includes forming said dam with a cross sectional joint hav1ng sub-divisional enclosed pressure, receiving spaces over its area, applying and holding d fferential pressures separately and respectively on such pressure receiving spaces, and in such relation to the stresses created by the ,water load that the stresses to which the joint section of the dam is subjected will be substantiall uniformly distributed across the face of t e joint area.

4. The method of building a concrete dam or the like, that includes formin said dam with a cross-sectional joint having sub-divisional enclosed spaces adapted to receive grouting, applying grouting material under difi'erent pressures, respectively to the several spaces, the differential grouting pressures being such that the stresses to which the joint section of the dam is subjected will be substantially uniformly distributed across the face ofthe cross sectional joint area, and maintaining the grout under such pressures until it sets.

5. The method of building a concrete dam or the like, that includes forming said dam with a cross-sectional joint having subdivisional enclosed spaces adapted to receive grouting, applying water to the several spaces respectively under difi'erent pressures, subsequently applying grouting to the several spaces respectively under different pressures,

said differential pressures on both the water and grout beingsuch that the stresses to which the oint section of the dam is subjected will be substantially uniformly distributed across the face of the joint area, and finally maintaining the grouting under such pressures until it sets.

6. In a concrete structure, such as a dam or the like, having sectional joints, sub-divisional grouting receiving spaces extending over the area of the joint, pressure resisting means separating the several grouting receiving spaces so as to prevent pass of pressure om one space to another, an each such space being relatively wide and open for the free reception of the grouting at substantially uniform pressure. 7

7. In a concrete structure, such as a dam or the like, having sectional joints, a grouting receiving .space within the area of the joint, and a pressure resisting barrier embedded in the walls of the joint and enclosing said space.

8. The method of building a concrete dam or the like, that includes forming said dam with a cross-sectional joint having sub-divisional enclosed spaces adapted to receive grouting, applying grouting material to the several spaces under differential pressures,

sures until it sets, the differential grouting pressures being such as to create, when added to the differential pressures created at the sub-divided joint spaces by the water load and the volumetric changes of the concrete due to setting, changes of temperature and moisture content, and time effect, a substantially uniform pressure over the entire face of each joint.

9. The method of building a concrete dam or the like, that includes forming said dam with a cross-sectional joint having sub-divisional enclosed spaces adapted to receive grouting, circulating water through said spaces, then applying rout material to the several spaces under. iiierential pressures, the pressures being such that the stresses to which that ortion of the structure is subjected will substantially uniformly distributed across the face of the oint area, and

finally maintaining the grout under such pressures until it sets.

10. The method of building a concrete dam or the like, that includes forming said dam with a cross-sectional joint having an enclosed space adapted to receive water or grouting under pressure, applying water under high pressure to said space until the concrete is substantially set, so as to open the joint as the concrete sets, subsequently applying grouting to the said space under substantia ly the same pressure, an maintaining the grouting under such pressure until its sets.

1 In witness that I claim the foregoing I have hereunto subscribed my name this fourteenth day of March, 1928.

I FREDBIK VOGT.

and maintaining the grout under such pres- 

